Efficient Bregman Iteration in fully 3D PET

Positron Emission Tomography reconstruction is ill posed. The result obtained with the iterative ML-EM algorithm is often noisy, which can be controlled by regularization. Common regularization methods penalize high frequency features or the total variation, thus they compromise even valid solutions that have such properties. Bregman iteration offers a better choice enforcing regularization only where needed by the noisy data. Bregman iteration requires a nested optimization, which poses problems when the algorithm is implemented on the GPU where storage space is limited and data transfer is slow. Another problem is that the strength of the regularization is set by a single global parameter, which results in overregularization for voxels measured by fewer LORs. To handle these problems, we propose a modified scheme that merges the two optimization steps into one, eliminating the overhead of Bregman iteration. The algorithm is demonstrated for a 2D test scenario and also in fully 3D reconstruction. The benefits over TV regularization are particularly high if the data has higher variation and point like features. The proposed algorithm is built into the TeraTomo (TM) system.